gives the derivative with respect to of the radial spheroidal function of the first kind.
- Mathematical function, suitable for both symbolic and numerical manipulation.
- For certain special arguments, SpheroidalS1Prime automatically evaluates to exact values.
- SpheroidalS1Prime can be evaluated to arbitrary numerical precision.
- SpheroidalS1Prime automatically threads over lists.
Examplesopen allclose all
Basic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at a singular point:
Numerical Evaluation (4)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number inputs:
Evaluate efficiently at high precision:
Plot the SpheroidalS1Prime function for integer orders:
Plot the SpheroidalS1Prime function for noninteger parameters:
Plot the real part of :
Plot the imaginary part of :
First derivative with respect to z:
Higher derivatives with respect to z:
Plot the higher derivatives with respect to z when n=10, m=2 and γ=1/3:
Compute the indefinite integral using Integrate:
Verify the anti-derivative:
Series Expansions (2)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
Taylor expansion at a generic point:
Find resonant frequencies for the Neumann problem in a prolate spheroidal cavity:
Determine the first few frequencies:
Possible Issues (1)
Spheroidal functions do not evaluate for half-integer values of and generic values of :